So I already ran some tests to make my data stationary. Differencing and box-cox transformation in particular. According to the augmented-dickey fuller test, after performing the above mentioned transformations, the data does not have a unit root but it is still not normally distributed. Can someone enlighten me about this?
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1$\begingroup$ stackoverflow.com/questions/14062635/… $\endgroup$– Karel MacekCommented Apr 9, 2015 at 8:32
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1$\begingroup$ Let the two sequences $(\ldots,0,0,0,\ldots)$ and $(\ldots,1,1,1,\ldots)$ have equal probabilities of $1/2$. Each component therefore has a Bernoulli(1/2) distribution--it's not Normal. Is your definition of "stationary" flexible enough to recognize this as a stationary process? If not, exactly what is your definition? $\endgroup$– whuber ♦Commented Apr 9, 2015 at 16:00
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$\begingroup$ Related question stats.stackexchange.com/q/38852/6633 $\endgroup$– Dilip SarwateCommented Apr 9, 2015 at 16:08
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2$\begingroup$ To answer briefly, stationary data need not be normal. Normality is not a requirement for stationarity (regardless of which definition -- strict stationarity or weak stationary -- you use). $\endgroup$– Richard HardyCommented Apr 9, 2015 at 18:36
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